$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 9x - 4$ and $ BC = 4x + 21$ Find $AC$.
A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {9x - 4} = {4x + 21}$ Solve for $x$ $ 5x = 25$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 9({5}) - 4$ $ BC = 4({5}) + 21$ $ AB = 45 - 4$ $ BC = 20 + 21$ $ AB = 41$ $ BC = 41$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {41} + {41}$ $ AC = 82$